In brief:
Get a 2nd opinion

The best way to prevent yeast infection is to avoid unnecessary antibiotics.

Proper treatment of lyme disease & other tick borne infections can usually be achieved in about 2-3 weeks - if treatment is prescribed >4 weeks consider a 2nd opinion with another expert (it never hurts to ask). Alert your doctor of any new symptoms of yeast asap rather than take a preventive antifungal for yeast.

In brief:
Get a 2nd opinion

The best way to prevent yeast infection is to avoid unnecessary antibiotics.

Proper treatment of lyme disease & other tick borne infections can usually be achieved in about 2-3 weeks - if treatment is prescribed >4 weeks consider a 2nd opinion with another expert (it never hurts to ask). Alert your doctor of any new symptoms of yeast asap rather than take a preventive antifungal for yeast.
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In my opinion you need input from an infectious diseases doctor with some experience in treating Lyme. If you received 4 wks of appropriate therapy and are not better, question the diagnosis, question whether future antibiotics are going to change anything, and whether further testing is warranted.